Is it possible to load and riggify FBX format from not Blender software?
Once imported into Blender a model is a model, regardless of origin or file format.

You should be able to edit, texture, apply materials, rig and animate, any model once inside Blender, whether it was imported in FBX, or not

What you should pay attention to is the quality of the modelling. The ability to be animated will depend largely on the quality and topology of the mesh.
A quad based geometry is preferable, avoid triangles, ngons and sculpted meshes.

The file format will only have influence on what type of data will be brought in with the model. Most likely any modifiers and optimizations done to the model with software specific features will be lost. You may also want to see if an un-
subdivided base mesh is provided, so you can subdivide yourself to the desired target levels.